Universe 2998 from The Wolfram Physics Project

6 steps

wm2998`wm2998`

signature

2₃→4₃

rule

{{{1, 2, 3}, {4, 5, 6}} -> {{1, 5, 7}, {1, 7, 4}, {2, 5, 4}, {8, 7, 5}}}

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Basic Evolution

Basic evolution:

[◼]	WolframModel

[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},6,"StatesPlotsList"]





Event-by-event evolution:

[◼]	WolframModel

[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"]





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},11,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},-2y.[n.]+y.[1+n.]0,y.[1]1,y.[2]3,y.[3]7[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

Result after

generations:

WolframModel[

]

["FinalStatePlot"]

Causal Graph

Causal graph:

WolframModel[

]

"CausalGraph",

Rule[

]



Layered rendering:

WolframModel[

]

["LayeredCausalGraph"]

Causal graph distance matrix:

MatrixPlotTransposeGraphDistanceMatrix

WolframModel[

]

["CausalGraph"],



Final State Properties

Hypergraph adjacency matrix:

MatrixPlotAdjacencyMatrix@CatenateMapUndirectedEdge@@@Subsets[#,{2}]&,

WolframModel[

]

["FinalState"],



Vertex degree distribution:

HistogramValuesCountsCatenateUnion/@

WolframModel[

]

["FinalState"],



Neighborhood volumes (ignoring directedness of connections):

volumes=

[◼]	RaggedMeanAround

Values

[◼]	HypergraphNeighborhoodVolumes



WolframModel[

]

["FinalState"],All,Automatic;

ListLogLogPlotvolumes,



Effective dimension versus radius:

ListLinePlot

[◼]	LogDifferences

[volumes],



Successive neighborhood balls around a random vertex:

[◼]	HypergraphNeighborhoods



WolframModel[

]

["FinalState"],4





Distance matrix:

distanceMatrix=GraphDistanceMatrixUndirectedGraph

[◼]	HypergraphToGraph



WolframModel[

]

["FinalState"];

MatrixPlotExp[-(distanceMatrix/.0None)],



Distribution of distances in the graph:

HistogramFlatten[distanceMatrix],



Spreading of Effects

Causal graph adjacency matrix:

MatrixPlotAdjacencyMatrix

WolframModel[

]

["CausalGraph"],



Neighborhood volumes in causal graph:

ListLogLogPlotValues

[◼]	GraphNeighborhoodVolumes



WolframModel[

]

["CausalGraph"],{1},



Other Evolution Orders

Random evolutions:

[◼]	WolframModel

[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},<|"MaxEvents"63|>,"FinalStatePlot","EventOrderingFunction""Random"]

[◼]	WolframModel

[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},MaxEvents63,FinalStatePlot,EventOrderingFunctionRandom]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},<|"MaxEvents"63|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}



[◼]	WolframModel

[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},MaxEvents63,EventOrderingFunction{OldestEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelOldestEdge],

[◼]	WolframModel

[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},MaxEvents63,EventOrderingFunction{LeastOldEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelLeastOldEdge],

[◼]	WolframModel

[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},MaxEvents63,EventOrderingFunction{LeastRecentEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelLeastRecentEdge],

[◼]	WolframModel

[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},MaxEvents63,EventOrderingFunction{NewestEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelNewestEdge],

[◼]	WolframModel

[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},MaxEvents63,EventOrderingFunction{RuleOrdering,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelRuleOrdering],

[◼]	WolframModel

[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},MaxEvents63,EventOrderingFunction{ReverseRuleOrdering,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelReverseRuleOrdering]

Graph Features of States

graph=

[◼]	HypergraphToGraph



WolframModel[

]

["FinalState"];

HistogramClosenessCentrality[graph],



Cycle properties:

EdgeCycleMatrix[UndirectedGraph[graph]]//MatrixPlot

Histogram[Length/@FindFundamentalCycles[UndirectedGraph[graph]]]

FindSpanningTree[UndirectedGraph[graph]]

‹ Registry of Notable Universe Models

wm2998wm2998

Basic Evolution

Causal Graph

Final State Properties

Spreading of Effects

Other Evolution Orders

Graph Features of States

wm2998`wm2998`